Market Power

Besanko and Braeutigam, CH 11

Hans Martinez

Western University

Market Power

  • When an individual agent can affect the price (or other outcome) that prevails in the market, the agent has market power

  • A monopoly market consists of a single seller facing many buyers

  • A monopsony market consists of a single buyer facing many sellers

Monopoly

  • In contrast to a perfectly competitive firm, a monopolist sets the market price of its product (market power)

  • The demand curve stops the monopolist from setting an infinitely high price by imposing a trade-off

    • The higher the price, the lower the quantity it sells
    • The lower the price, the higher the quantity it sells

Monopolist’s Demand Curve

  • The monopolist’s demand curve is the market demand curve

  • The profit-maximizing monopolist’s problem is finding the optimal trade-off between volume and margin (difference between price and marginal cost)

Monopolist’s Problem

The monopolist’s profit-maximization problem : \[ \begin{aligned} \max_Q \pi(Q)&=TR(Q)-TC(Q) \\ \text{s.t. }& TR(Q)=QP(Q) \end{aligned} \qquad(1)\]

  • where \(P(Q)\) is the inverse market demand

Optimality Condition

  1. Profits are maximized at \(Q^*\) such that \(MR(Q^*)=MC(Q^*)\)

  2. Slope of the \(MC\) curve exceeds the slope of the \(MR\) curve

Optimality Condition

Figure 1

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Marginal Revenue

  • \(MR(Q)=\frac{d TR(Q)}{dQ}\)
    • \(=P+Q\frac{dP(Q)}{dQ}\)
  • \(MR = \frac{\Delta TR}{\Delta Q}=\frac{P\Delta Q+Q\Delta P}{\Delta Q}\)
    • \(=P+Q\frac{\Delta P}{\Delta Q}\)

Marginal Revenue

Competitive firms is not affected by the change in price due to its change in output

Marginal Revenue

  • Marginal revenue has two parts:

    • \(P\): increase in revenue due to higher volume -the marginal units
    • \(Q(dP(Q)/dQ)\): decrease in revenue due to reduced price of the inframarginal units (negative)
  • The marginal revenue is less than the price the monopolist can charge to sell that quantity for any \(Q\ge0\) because \(dP(Q)/dQ\le0\)

  • MR can be positive or negative

Marginal Revenue

  • \(AR(Q)=TR(Q)/Q\)
    • \(=QP(Q)/Q=P(Q)\)
  • \(MR(Q) \le P(Q)\)
    • \(\implies MR(Q) \le AR(Q)\)

Profit-Maximization Condition

Suppose the monopolist faces a linear demand curve

\[ P(Q)=a-bQ \]

Then, the revenue function is

\[ TR(Q)=QP(Q)=aQ-bQ^2 \]

and the marginal revenue function is

\[ MR(Q)=a-2bQ \]

Profit-Maximization Condition

Monopoly vs Competitive Market

  • \(P_M>MC_M\), in general \(P_M > P_{PC}\)
  • \(Q^*_{M} < Q^*_{PC}\)
  • \(\pi_{M}\ge0\)
  • Consumers are worse off but the firm is better off. What’s best?

Monopoly is not Pareto Efficient

  • Pareto Efficiency: There is no way to make someone better off without making somebody else worse off

  • Inverse demand curve: At each level of output, \(P(Q)\) measures how much people are willing to pay for an additional unit of the good

Monopoly is not Pareto Efficient

  • Since \(P(Q)\ge MC(Q)\) for all output levels between \(Q_M\) and \(Q_C\)

  • There is a range of consumers that are willing to pay \(\bar P\) for an extra unit of output, such that \(P(Q)>\bar P> MC(Q)\) (area under demand curve between \(Q_M\) and \(Q_C\) and above the \(MC(Q)\))

Inefficiency of Monopoly

  • Any of these consumers would be better off because they are willing to pay \(P(Q)\) but the extra unit of output is sold at \(\bar P < P(Q)\)

  • Likewise, the firm would be better off because it cost \(MC(Q)\) to produce the extra unit of output and the firms sold it for \(\bar P > MC(Q)\)(all the other units of output are being sold for the same price \(P_M\) as before)

  • We found a Pareto improvement!

Inefficiency of Monopoly (continued)

Welfare Economics of Monopoly

  • How inefficient is a Monopoly?

  • Compare changes in producer’s and consumer’s surplus from a movement from Monopoly to Perfect Competition

  • Change in producer’s surplus —firm’s profits— measures how much the owners would be willing to pay to get the higher price under monopoly

  • Change in consumers’ surplus measures how much the consumers would have to be paid to compensate them for the higher price

Deadweight Loss of Monopoly

Deadweight Loss of Monopoly

  • Producer loses A, but gains C

  • Consumer gains A and B

  • A is just a transfer; total surplus does not change

  • B+C is a real gain in surplus

  • Deadweight Loss of Monopoly (B+C) measures how much worse off people are paying the monopoly price than paying the competitive price

  • DWL values each unit of lost output at the price that people are willing to pay for that unit

No Unique Supply Curve for Monopolists

  • In Competitive Markets, \(P=MC(Q)\), there is a unique relationship between the quantity produced by the firm and price \(Q=MC^{-1}(P)\)

  • In Monopoly, \(P+Q\frac{dP(Q)}{dQ}=MC(Q)\)

  • Depending on the shape of the demand curve,\(\frac{dP(Q)}{dQ}\), the monopolist might produce the same quantity at two different prices or produce different quantities at the same price

    • no unique relationship between \(Q\) and \(P\), \(\implies\) no unique supply curve

No Unique Supply Curve

Price Elasticity of Demand

\[ \begin{aligned} MR(Q)&=P+Q\frac{dP(Q)}{dQ} \\ &=P\left(1+\frac{Q}{P}\frac{dP(Q)}{dQ} \right)\\ &=P\left(1+\frac{1}{\frac{P}{Q}\frac{dQ}{dP}}\right)\\ &=P\left(1+\frac{1}{\epsilon_{Q,P}}\right) \\ &=P\left(1-\frac{1}{|\epsilon_{Q,P}|}\right) \text{(because $\epsilon_{Q,P}<0$)} \end{aligned} \]

➤ Elasticity Refresher

Price Elasticity of Demand

Table 1: Elasticity of Demand
Elasticity Marginal Revenue Output and Profits
\(|\epsilon_{Q,P}|<1\) \(MR<0\) Reducing output increases revenue and reduces cost, so profits necessarily increase
\(|\epsilon_{Q,P}|\ge1\) \(MR\ge 0\) Increasing output increases revenue but cost increase, optimal output lies here
\(|\epsilon_{Q,P}|=\infty\) \(MR=P\) Competitive case

➤ Optimality Condition Graph

Elastic Part of the Curve

  • Monopolists will never choose to operate where the demand is inelastic
  1. \(MC\ge0\), at the optimum \(MR=MC\ge0\), but \(|\epsilon_{Q,P}|<1 \implies MR <0\)

  2. Any point were \(|\epsilon_{Q,P}|<1\) cannot be a profit maximum, since the monopolist could increase profits by producing less output

Pricing Rule

Profit maximizing condition is \(MR = MC\) with \(P^*\) and \(Q^*\)

\[ \begin{aligned} 𝑀𝑅(𝑄^∗ )&=𝑀𝐶(𝑄^∗ ) \\ 𝑃^∗ \left(1-\frac{1}{|\epsilon_{𝑄,𝑃}|}\right)&=𝑀𝐶(𝑄^∗) \end{aligned} \]

Rearranging and setting MR(Q) = MC(Q) \[ \frac{(𝑃^∗−𝑀C^∗)}{𝑃^∗} =\frac{1}{ |\epsilon_{𝑄,𝑃}| } \]

Inverse elasticity pricing rule (IEPR): The less price elastic the demand, the higher the optimal markup

Demand Elasticity

Market B is less price elastic than A, thus the markup is higher in B than in A

Market Power

  • When a firm can exercise some degree of control over its price in the market, we say that it has market power

  • Monopolists or producers of differentiated products will, in general, charge prices that exceed their marginal cost

  • A natural measure of market power is \((P − MC)/P\)

    • Lerner Index
  • The Lerner Index is zero for a perfectly competitive industry. It is positive for any industry that departs from perfect competition.

Market Power

  • The IEPR tells us that in the equilibrium of a monopoly market, the Lerner Index will be inversely related to the market price elasticity of demand.

  • An important driver of the price elasticity of demand is the threat of substitute products outside the industry

  • If a monopoly market faces strong competition from substitute products, the Lerner Index can still be low. In other words, a firm might have a monopoly, but its market power might still be weak.

Why Monopolies Exist?

  • A market is a natural monopoly if the total cost incurred by a single firm producing output is less than the combined total cost of two or more firms producing this same level of output among them

  • Necessary conditions

    • Economies of scale
    • Demand

Natural Monopoly

It is cheaper for 1 firm to produce 9 than for two to produce 4.5

Barriers to entry

  • Factors that allow an incumbent firm to earn positive economic profits while making it unprofitable for newcomers to enter the industry

  • Structural barriers to entry occur when incumbent firms have cost or demand advantages that would make it unattractive for a new firm to enter the industry

  • Legal barriers to entry exist when an incumbent firm is legally protected against competition

  • Strategic barriers to entry result when an incumbent firm takes explicit steps to deter entry

Monopsony

  • A monopsony market consists of a single buyer facing many sellers

  • The monopsonist’s profit maximization problem:

    • \(\max \pi = TR – TC = Pf(L) – w(L)L\)
    • where: \(Pf(L)\) is the total revenue for the monopsonist
    • and \(w(L)L\) is the total cost
  • The monopsonist’s profit maximization condition:

    • \(MRP_L = ME_L\)
    • \(P \times MP_L = dTC/dL\)
    • \(P (dQ/dL) = w + L (dw/dL)\)

Monopsony

Inverse Elasticity Pricing Rule

  • Monopsony equilibrium condition results in:
    • \((MRP_L−w)/w=1/\epsilon_{L,w}\)
    • where: \(\epsilon_{L,w}\) is the price elasticity of labor supply, \((w/L)(dL/dw)\)

Monopsony DWL

  • Consumer (Monopsony firm) gets A+B+C

  • Producer (Workers) gets D

  • The deadweight loss is F+G

Problems

Comparative Statics

  • Shifting intercept up or down (linear curves)
    • Shifts in demand
    • Shifts in MC
      • Upward sloping
      • Downward sloping
  • Constant MC and linear demand (Monopoly Midpoint Pricing Rule)

Monopolies with Multiple Plants and Markets

  • Two plants, one demand
    • Cartel: A group of producers that collusively determines the price and output in a market
    • Same problem: allocating output across its plants
  • Two markets (demand curves), one price

Taxes and Monopolies

Monoposony and the Minimum Wage

Appendix

Price Elasticity of Demand REVIEW

  • The price elasticity of demand is the percentage change in quantity demanded due to a one-percent change in the price of the good

  • \(\epsilon_{Q,P}=\frac{Δ𝑄/𝑄}{Δ𝑃/𝑃}=\frac{Δ𝑄}{Δ𝑃}\frac{𝑃}{𝑄}\)

  • Elasticity is not the slope:

    • Slope measures the absolute change in quantity due to one-unit change price \((Δ𝑄⁄Δ𝑃)\)

    • Elasticity measures the relative (or percentage) change in quantity due to one percent change price

Price Elasticity of Demand

\(ϵ_{Q,P}\) Classification Meaning
\(|ϵ_{Q,P}|<1\) Inelastic demand Quantity demanded is relatively insensitive to price.
\(|ϵ_{Q,P}|\ge1\) Elastic demand Quantity demanded is relatively sensitive to price.
\(|ϵ_{Q,P}|=\infty\) Perfectly elastic demand Any increase in price results in quantity demanded decreasing to zero, and any decrease in price results in quantity demanded increasing to infinity.

Price Elasticity of Demand

Elasticity - Linear Demand

  • \(P=\frac{a}{b}-\frac{Q}{b}\)

  • \(𝜀_{Q,P}=−b(𝑃/𝑄)\)

  • Elasticity falls from 0 to \(-\infty\) along the linear demand curve, but the slope is constant

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